Amplitude spectrum compensation and phase spectrum correction of seismic data based on the generalized S transform
Zhou Huai-Lai1,2,3, Wang Jun4, Wang Ming-Chun5, Shen Ming-Cheng3, Zhang Xin-Kun3, and Liang Ping6
1. State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, CDUT, Chengdu 610059, China.
2. Key Lab of Earth Exploration & Information Techniques of Ministry of Education, CDUT, Chengdu 610059, China.
3. College of Geophysics, Chengdu University of Technology, Chengdu 610059, China.
4. Institute of Sedimentary Geology, Chengdu University of Technology, Chengdu 610059, China.
5. Exploration and Development Institute of Bohai Oil Field of CNOOC Co., Ltd Tianjin Branch, Tianjing 300452, China.
6. College of Energy Resource, Chengdu University of Technology, Chengdu 610059, China.
Abstract：
We propose a method for the compensation and phase correction of the amplitude spectrum based on the generalized S transform. The compensation of the amplitude spectrum within a reliable frequency range of the seismic record is performed in the S domain to restore the amplitude spectrum of reflection. We use spectral simulation methods to fit the time-dependent amplitude spectrum and compensate for the amplitude attenuation owing to absorption. We use phase scanning to select the time-, space-, and frequency-dependent phases correction based on the parsimony criterion and eliminate the residual phase effect of the wavelet in the S domain. The method does not directly calculate the Q value; thus, it can be applied to the case of variable Q. The comparison of the theory model and field data verify that the proposed method can recover the amplitude spectrum of the strata reflectivity, while eliminating the effect of the residual phase of the wavelet. Thus, the wavelet approaches the zero-phase wavelet and, the seismic resolution is improved.
ZHOU Huai-Lai,WANG Jun,WANG Ming-Chun et al. Amplitude spectrum compensation and phase spectrum correction of seismic data based on the generalized S transform[J]. APPLIED GEOPHYSICS, 2014, 11(4): 468-478.
[1]
Bracewell, R. N., 2000, The Fourier integral and Its Applications, 3rd ed., [M]. Boston: McGraw-Hill, U. S. A, 256-260.
[2]
Carlos, A. M., and Margrave, G. F., 2005, Phase correction in Gabor deconvolution: 75th Annual International Meeting, SEG, Expanded Abstracts, 2173-2176.
[3]
Chen, B. Y., Chen, M. W., and Yi, W. Q., 1997, Time and space and subsection frequency phase correction: Oil Geophysical Prospecting (in Chinese), 32(1), 103-108.
Cohen, L., 1995, Time-Frequency Analysis: Theory and Applications [M]. N j: Prentice Hall, Inc., U. S. A, 25-27.
[6]
Durak, L., and Arikan, O., 2003, Short-time Fourier transform: two fundamental properties and optimal implementation: IEEE Trans. on signal Processing, 51(5), 1231-1242.
[7]
Ferber, R., 2005, A filter bank solution to absorption simulation and compensation: 75th Annual International Meeting, SEG, Expanded Abstracts, 2170-2172.
[8]
Gabor, D., 1946, Theory of Communication: Journal of IEEE, 93(3), 429-457.
[9]
Gao, J. H., Chen, W. C., Li, Y. M., and Tian, F., 2003, Generalized S transform and seismic response analysis of thin interbeds: Chinese Journal of Geophysics (in Chinese), 46(4), 526-532.
[10]
Gao, S. W., Zhou, X. Y., and Cai, J. M., 2001, Surface-consistent phase correction for reflection wave: Oil Geophysical Prospecting (in Chinese), 36(4), 480-487.
[11]
Levy, S., and Oldenburg, D. W., 1982, The deconvolution of phase-shifted wavelets: Geophysics, 47(9), 1285-1294.
[12]
Levy, S., and Oldenburg, D. W., 1987, Automatic phase correction of common-midpoint stacked data: Geophysics, 52(1), 51-59.
[13]
Li, K. P., Li, Y. D., and Zhang, X. G., 2000, A method to compensation earth filtering based on wavelet packet: Chinese Journal Of Geophysics, 43(4), 542-549.
[14]
Li, Q. Z., 1994, The road to Precision Prospecting—High Resolution Seismic Prospecting System Analysis (in Chinese).: Petroleum Industry Press, Beijing, 89-92.
[15]
Li, T. C., He, Y. M., Sun, J., Xu, Z. Q., Liu, J. M., Qin, D. M., and Zhu, J. M., 2010, Research and application of frequency amplitude compensation by frequency decomposition based on generalized S transformation: Computing Techniques for Geophysical and Geochemical exploration(in Chinese), 36(6), 583-586.
[16]
Liu, X. W., Nian, J. B., and Liu, H., 2006, Generalized S-transform based seismic attenuation analysis: Progress in Exploration Geophysics (in Chinese), 29(1), 14-19.
[17]
Ma, J. Q., Li, Q. C., and Wang, M. D., 2010, Stratigraphic absorption-compensation based on the generalized S-transform: Coal Geology and Exploration (in Chinese), 38(4), 65-68.
[18]
Mansinha, L., Stockwell, R. G., and Lowe, R. P., 1997, Pattern analysis with two dimensional spectral localization: Application of two dimensional S-transform: Physics Section A, 239(3), 286-295.
[19]
Margrave, G. F., 1998, Theory of nonstationary linear filtering in the Fourier domain with application to time-variant filtering: Geophysics, 63, 244-259.
[20]
Margrave, G. F., and Lamoureux, M. P., 2001, Gabor deconvolution:CREWES Research Report. 13, 241-276.
[21]
McFadden, P. D., Cook, J. G., and Forster, L. M., 1999, Decomposition of gear vibration signals by generalized S-transform: Mechnical Systems and Signal Process, 13(4), 691-707.
[22]
Mirko van der Baan and Fomel, S., 2009, Nonstationary phase estimation using regularized local kurtosis maximization: Geophysics, 74(6), A75-A80.
[23]
Mirko van der Baan, 2012, Bandwidth enhancement: Inverse Q filtering or time-varying wiener deconvolution: Geophysics, 77(4), V133-V142.
[24]
Peng, C., Zhu, S. J., Sun, J. K., Lin, S. W., Chang, X., and Zhao, J. M., 2007, Dynamic seismic wavelet estimation: Petroleum Geology and Oilfield Development in Daqing (in Chinese), 26(5), 125-128.
[25]
Pinnegar, C. R., and Mansinha, L., 2003, The S-transform with windows of arbitrary and varying shape: Geophysics, 68(1), 381-385.
[26]
Pinnegar, C. R., and Mansinha, L., 2003, Time local spectral analysis for non-stationary time series: the S-transform for noisy signals: Fluctuation and Noise Letters, 3(3), 357-364.
[27]
Ricker, N. H., 1977, Transient waves in visco-elastic media: Elsevier Science Publ Co, 123-136.
[28]
Rioul, O., and Vetterli, M., 1991, Wavelets and signal processing: IEEE Signal Processing, 8(4), 14-38.
[29]
Rosa, A. L. R., and Ulrych, T. J., 1991, Processing via spectral modeling: Geophysics, 56(8), 1244-1251.
[30]
Song, Z. P, Li, J. J., and Zhang, L. P., 2004, Pre-stack constant phase correction: Petroleum Geology and Oilfield Development in Daqing (in Chinese), 23(2), 69-70.
[31]
Stockwell, R. G., Mansinha, L., and Lowe, R. P., 1996, Localization of the complex spectrum: the S transform: IEEE Transactions on signal processing, 44(4), 998-1001.
[32]
Sun, C. Y., 2000, Spectrum modeling method and its application to seismic resolution improvement: Oil Geophysical Prospecting (in Chinese), 35(12), 27-34.
[33]
Wang, Y. H., 2002, A stable and efficient approach of inverse Q filtering: Geophysics, 67(2), 657-663.
[34]
Wang, Y. H., 2006, Inverse Q filtering for seismic resolution enhancement: Geophysics, 71(3), 51-61.
[35]
Wang, Y. H., 2007, Seismic time-frequency spectral decomposition by matching pursuit: Geophysics, 72, V13-V20, doi:10.1190/1.2387109.
[36]
Wang, Y. H., 2010, Multichannel matching pursuit for seismic trace decomposition: Geophysics, 75, V61-V66.
[37]
Yu, S. P., 1993, The High Resolution Seismic Processing (in Chinese) [M]. Beijing: Petroleum In dustry Press, China, 162-164.
[38]
Yuan, X. G., Song, S. G., Zhang, J. G., Hou, M. Z., and Yang, J. H., 2001, Treatment of stacked seismic data with multi-resolution frequency-amplitude compensation: Journal of Central South University of Technology (in Chinese), 32(3), 224-226.
[39]
Zhao, B., Yu, S. P., Nie, X. B., and Huang, X. N., 1996, Spectral-modeled deconvolution and its application: Oil Geophysical Prospecting (in Chinese), 31(1), 101-115.
2014, Vol. 11 
